Unwanted pentagon in unwrap
The first thing would be to see if the mesh has a non-square face (ie, with 5 vertices) and fix it if it does. If it does and you want do be lazy, simply add one vertex in the middle and use that to make triangles. 

(Faces that are made of more than four vertices are known to cause problems in weird places, so making a habit of removing them and keeping a good topology will make things easier. I think blender for the most part doesn't have a problem with it except for edges and faces that do have the same location.)

The best way to fix the uv map is probably to make a new one. I would recommend you first use it with a checker texture to find any weirdness first, so you might discover any other problems you might have missed.